Inference for post-change mean by a CUSUM procedure |
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| Institution: | 1. Institute of Water Resources and Hydro-electric Engineering, Xi''an University of Technology, Xi''an 710048, People''s Republic of China;2. School of Life Science and Key Laboratory of Clean Dyeing and Finishing Technology of Zhejiang Province, Shaoxing University, Huancheng West Road 508, Shaoxing, 312000, People''s Republic of China;3. Shaoxing City Environmental Monitoring Station, Shaoxing 312000, People''s Republic of China;1. Department of Biochemistry, Falavarjan Branch, Islamic Azad University, Isfahan, Iran;2. Department of Chemistry, Graduate University of Advanced Technology, Kerman, Iran;3. Department of Chemistry, Indian Institute of Technology Roorkee, Roorkee 247667, India;4. Center for Environment and Water, The Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia;5. Department of Applied Chemistry, University of Johansburg, Johansburg, South Africa;1. Key Laboratory of Colloid and Interface Chemistry, Shandong University, Ministry of Education, Jinan 250100 PR China;2. College of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, PR China |
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| Abstract: | In this paper, the inference problem for the post-change mean is considered after a change is detected by a CUSUM process in a sequence of independent normal variables. The change-point is estimated as the maximum likelihood estimate at the reference value and the post-change mean is estimated as the sample mean after the change-point estimate. By assuming the change-point is large and the monitoring limit approaches infinity, the first-order bias of the post-change mean estimate and a corrected asymptotic normal pivot are derived conditioning on that a change is detected. Local approximations for small reference value and post-change mean are obtained for numerical evaluation. |
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